1. Field of the Invention
The invention relates to integrated circuit fabrication, and more particularly to methods for determining the average critical area of a particular layout.
2. Description of Related Art
As VLSI technology moves to deep submicron, manufacturability and yield related issues become increasingly important. Yield loss can be caused by many factors. One important factor is random defect yield loss, which is related to the yield loss caused by contamination particles. The design related parameter required for modeling random defect yield is sometimes called the critical area.
Critical Area measures a design's sensitivity to the random particle defects. Much work has been done on extracting and calculating the critical area for a given design layout. The main approaches fall into the two main categories: Shape Expansion based methods and Monte Carlo methods. Conventional shape expansion based methods generally attempt to calculate the critical area contributed by each object and for each particular defect size of interest. For each defect size, the method approximates the geographic union of the critical area contributions of all the objects. The result is then averaged over all the defect sizes, weighted by the defect size distribution.
One problem with the conventional shape expansion methods is that calculation of a geographic union can be extremely time consuming. Some methods approximate the geographic union, but only at the expense of accuracy. Other methods do not even attempt to approximate the geographic union, and simply add all the critical area contributions together. The latter variation creates significant inaccuracies because overlapping regions are counted twice or more: once for each object that includes the region in its critical area contribution. Many conventional shape expansion methods also suffer because they require a separate critical area calculation for each defect size of interest. Because each critical area calculation is so expensive, the number of discrete defect sizes for which it is calculated is often reduced, thereby degrading accuracy of the results. If accuracy is to be improved by increasing the number of discrete defect sizes at which the critical area calculation is made, then runtimes can easily become prohibitive. Another problem with conventional shape expansion methods is that there is no explicit formula available for total critical area. Thus it cannot be used to evaluate critical area as part of cost function for layout optimization.
In Monte Carlo based methods, a generator generates random defects with their sizes following the given defect size distribution function. Since the Monte Carlo based methods do not need to limit themselves to any specific defect size, they do not suffer from accuracy degradation due to insufficient numbers of defect sizes tested. But accurate estimation may still require huge runtimes due to the need to test huge numbers of randomly generated defects.
Embodiments of the present invention can avoid the above problems and others by deriving an explicit formula for a weighted average “pseudo-critical area” contributed by each object in the layout region under study. Preferably the weighted average pseudo-critical areas depend only on parameters of the layout, all of which can be extracted during a single sweep through the objects in the region. The weighted average pseudo-critical area preferably already accounts for all defect sizes of interest, so it is not specific to any individual defect size. It is therefore unnecessary to perform the calculation separately for each of many defect sizes. The weighted average pseudo-critical area preferably is defined also such that regions that might, under conventional definitions, be included in the critical area contributed by more than one object, are allocated to such objects in a non-overlapping manner. Calculating the geographic union of the weighted average pseudo-critical areas in such an embodiment therefore can be as simple as summing them. The final result for total weighted average critical area can be another explicit formula, as a function of layout parameters only.